A Queueing System for Modeling a File Sharing Principle

TL;DR

This paper models a file sharing system using a queueing approach with dynamic servers, analyzing its transient behavior and phase transition from congestion to idleness through urn and ball scaling methods.

Contribution

It introduces a novel queueing model with a random number of servers for file sharing and derives asymptotic scaling results for its transient behavior.

Findings

Derived scaling results for the queueing system.

Compared asymptotic analysis with simulation data.

Identified the transition point from congestion to idleness.

Abstract

We investigate in this paper the performance of a simple file sharing principle. For this purpose, we consider a system composed of N peers becoming active at exponential random times; the system is initiated with only one server offering the desired file and the other peers after becoming active try to download it. Once the file has been downloaded by a peer, this one immediately becomes a server. To investigate the transient behavior of this file sharing system, we study the instant when the system shifts from a congested state where all servers available are saturated by incoming demands to a state where a growing number of servers are idle. In spite of its apparent simplicity, this queueing model (with a random number of servers) turns out to be quite difficult to analyze. A formulation in terms of an urn and ball model is proposed and corresponding scaling results are derived. These asymptotic results are then compared against simulations.